A151310 Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0) and consisting of n steps taken from {(-1, -1), (-1, 1), (-1, 0), (0, 1), (1, -1), (1, 1)}

1, 2, 9, 37, 181, 869, 4430, 22640, 118808, 627275, 3358307, 18087833, 98248087, 536372711, 2945032779, 16237200915, 89896571332, 499383074373, 2783038880080, 15552412965005, 87134774936870, 489297438647055, 2753406974342080, 15523739339340106, 87677875795392958, 496006562740402954

Offset

0,2

Links

Robert Israel, Table of n, a(n) for n = 0..250

M. Bousquet-Mélou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387.

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

Maple

steps:= [[-1, -1], [-1, 1], [-1, 0], [0, 1], [1, -1], [1, 1]]:
f:= proc(n, p) option remember; local t;
  if n <= min(p) then return 6^n fi;
  add(procname(n-1, t), t=remove(has, map(`+`, steps, p), -1));
end proc:
map(f, [$0..100], [0, 0]); # Robert Israel, Jun 11 2019

Mathematica

aux[i_Integer, j_Integer, n_Integer] := Which[Min[i, j, n] < 0 || Max[i, j] > n, 0, n == 0, KroneckerDelta[i, j, n], True, aux[i, j, n] = aux[-1 + i, -1 + j, -1 + n] + aux[-1 + i, 1 + j, -1 + n] + aux[i, -1 + j, -1 + n] + aux[1 + i, -1 + j, -1 + n] + aux[1 + i, j, -1 + n] + aux[1 + i, 1 + j, -1 + n]]; Table[Sum[aux[i, j, n], {i, 0, n}, {j, 0, n}], {n, 0, 25}]

Crossrefs

Sequence in context: A150990 A150991 A150992 * A000663 A364088 A218942

Adjacent sequences: A151307 A151308 A151309 * A151311 A151312 A151313

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved